Tip #1: The quieter side of Mount Rigi.
Take a boat to Vitznau and connect to the Rigi train. Get off at Rigi Staffelhöhe. Climb to the top of Rotstock, drop down to First, and take in the fantastic view of Lake Lucerne as you follow the Felsenweg on the south side of Schild. Climb to the top of Dosse for more great views, drop to Hinterdosse, and hike up to Rigi Scheidegg. Take the gondola down to Kräbel and the train down to Arth-Goldau and back to Lucerne.
This is a short and relatively easy hike. Allow at least half a day. By Rigi standards it is fairly quiet because the vast majority of people flock to the Rigi Kulm area.
Tip #2: The scenic ridge leading up to Mount Pilatus.
Board a train to Entlebuch and connect to the postal bus to Gfelle. Follow the signage to Risetestock and Blaue Tosse, then continue along the scenic ridge trail all the way to Pilatus. Take the Pilatus train down to Alpnachstadt and the train back to Luzern.
This is a very long and relatively strenuous hike. Allow a whole day. It is best to take the earliest train and bus combo in the morning and plan to catch the very last Pilatus train down in the evening.
Tip #3: The Melchsee Frutt plateau.
The Melchsee Frutt plateau is a great hiking destination only 90' from Lucerne. Board a train to Sarnen, connect to a postal bus to Stöckalp, and take the gondola up to the plateau. There is a wide array of hiking options at Melchsee Frutt ranging from family walkies to freaky rock climbing experiences. Dad's personal pick is the hike to the top of Hochstollen by way of Abgschütz (very strenuous and only if you're not afraid of heights; only with perfectly dry weather conditions). Mom prefers less demanding viewpoints such as the Bonistock and the Balmeregghorn.
One more tip: the very finest maps in Switzerland can be perused and outprinted for free at map.wanderland.com.
Dear Gail, I hope you'll be able to bring Bertie next time!